An object starts at rest and experiences a constant acceleration of 4 m/s² for 3 seconds.

Sketch the acceleration-time graph for this object.

1. What was the initial velocity of the object?

2. What was the velocity of the object after 1 second?

3.What was the velocity of the object after 2 seconds?

4.What was the velocity of the object after 3 seconds?

5. Sketch the velocity-time graph for this object.

6. What was the average velocity of the 1st second?

7.What distance did the object travel in the 1st second?

8. What was the average velocity of the 2nd second?

9. What distance did the object travel in the 2nd second?

10.What was the average velocity of the 3rd second?

11. What distance did the object travel in the 3rd second?

12.Sketch the position-time graph for this object.

13.What was the displacement of the object?

14.What was the distance travelled by the object?​

It is to be noted that the marginal cost of increasing production from 5,000 units to 6,000 units, given the information provided, is: "$0.10" (Option D)

The marginal cost in economics is the change in total cost that occurs when the amount produced is increased or the cost of producing more quantity.

Mathematically, it is expressed as:

MC= ΔC/ ΔQ

Where:

MC  = marginal cost

ΔC = change in cost; and

Δ Q = change in quantity

The solution is derived as follows:

Given that:

Total Cost = Fixed cost + Variable cost  

Where the problem is defining the marginal cost of upping production from 5000 units to 6000 units.

In the attached table, the Second Row and Third Row respectively indicate increasing production from 5000 units to 6000 units.

In the Second Row, where the number of employees is 20, the output is 5000 units and the Total cost is $2200

Since Total cost = Fixed cost + Variable cost

Therefore, Total cost  = $2000 + $200 = $2200

In the Third Row, when the number of employees is 30, the output is 6000 units, and the Total cost is $2300

hence the Total Cost = $2000 + $300 = $2300

So, Marginal Cost =

Change in total cost/change in output units

Where change in Total cost

= Third Row total cost - Second Row total cost

= $2300 - $2200

= $100

and where Change in output units

= Third Row output units - Second Row output units

= 6000 units - 5000 units

= 1000 units

It is verified that the change in total cost is $100 and the change in output units is 1000 units.

Hence, the Marginal cost is:

MC - Change in total cost / Change in output units

= $100 / 1000 units  

= $0.10

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Full Question:

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Answer:
Highlighted words are the correct answer

A light year is the amount of time it takes for light from the Sun to reach the Earth.

True

False, a light year is the length light travels in a year

The ozone layer is important to human life because it protects people from:

microwaves.

gamma rays.

ultraviolet light rays.

None of the choices are correct.

UVA and UVB rays can cause skin damage and skin cancer.

True

False

Which of the following chemicals destroys the ozone layer?

CFCs

gasoline

hydrogen

All of the choices are correct.

The Milky Way is 100,000 light years in size.

True

False

All stars die out after becoming white dwarfs.

True

False

Black holes:

are the brightest objects in space.

are the most well understood objects in space.

pulse in a regular pattern. - only some pulse in a regular pattern though

None of the choices are correct.

They will feel equally hot or cold at the same temperature.

What do you mean by temperature?

Temperature is a physical parameter that describes how hot stuff or radiation is. There are 3 different types of temperature scales: those described in regards to the average translational kinetic energy per freely moving microscopic substance in a body, such as a atom, compound, or anion, such as the SI scale; those that rely solely on purely macroscopic properties and thermodynamic principles, such as Kelvin's original definition; and those that are not defined by theoretical principles, but are defined by convenient empirical properties of particulate matter.  

If they are the same temperature as the area of your body that is touching them, they will feel equally hot or cold. There will be no heat movement if the wood and iron at the same temperature as the skin, and the iron's higher thermal conductivity will be irrelevant. The specific temperature cannot be specified because if you touch the materials with your fingertips, the wood and iron must match that temperature, and if you test them with your tongue, which is often considerably warmer than your hands, the wood and iron must be warmer.

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Answer:

1.044 m/s^2

Explanation:

Fcosθ - u(mg - Fsinθ) = ma = 185cos28 - 0.3(47.5*9.81 - 185sin28) = 49.61N

a = 1.044

The average velocity is 2 meters/second. Option B.

Explanation:

This average velocity can be found using the following formula:

v = x / DT

where:

x = displacement = 18 [meters]

dt = time interval = 9 [seconds ]

v = 18 / 9

v = 2 [m/s]

The average velocity of a particle moving from one point to another over a time interval is equal to the ratio of the displacement between the two points to the time it takes the particle to move that displacement. To find the average speed take the total distance traveled divided by the time interval. To find the average velocity. Since the displacement is always less than or equal to the distance traveled, the magnitude of the average velocity is always less than or equal to the average velocity.

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3.13×10^2 metre  is the wavelength associated with this bullet.

[tex]\lambda=(h)/(mv)[/tex]

Here, lambda   is the wavelength, m   is the mass, v  is the velocity of the particle, and h is Planck's constant

The mass of a rifle bullet is 1.50g  and its velocity is 7×10^2 mph

First convert the values to SI units as follows:

[tex][m=1.50 g*1kg/10^3g,[=1.50 *10^-3kg][/tex]

[tex][v=7.00 *10^2mph*(0.447m/s/1mph],[=3.13*10^2m/s][/tex]

De Broglie wavelength refers to the wavelength of a wave that is connected to a moving particle, such as the matter-wave or de Broglie wave. It is derived from: =h/mv In this equation, m stands for the particle's mass, v for its speed, and h for the Planck constant.

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The force required by the curler will be 30 N

we see that the stone is pushed from rest to a certain velocity

initial velocity (u) = 0 m/s

final velocity (v) = 3 m/s

mass of the stone (m) = 20 kg

Time for which the stone is pushed (t) = 2 s

Now , for calculating the force required (without taking into account the friction)  we first need to calculate the acceleration

therefore , a = [tex]\frac{v-u}{t}[/tex]

     a = (3- 0)/ 2

      a = 1.5 m/s²

Now , we know that

Force = mass x acceleration

F  = 20 x 1.5

F =  30 N '

So the force required will be 30 N .

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The average angular acceleration of a Blu-ray disc is 0.089 rad/s².

Angular acceleration refers to the time price of exchange of angular speed. As there are types of angular velocity, namely spin angular velocity and orbital angular velocity, Angular speed is the rate of change of angular displacement and angular acceleration is the rate of trade of angular pace.

Angular Acceleration is described as the time rate of change of angular velocity. it is usually expressed in radians in keeping with second in line with second. as a result, α = d ω d t. Angular acceleration is also known as rotational acceleration.

t = time duration = 6 h = 6 x 3600 sec

α = angular acceleration = (Wmax - Wmin )/t = (315 - 121)/(6 x 3600 ) = 0.089 rad/s²

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As a result, neither the astronauts nor the others sharing the space station can feel the force that supports them from the structure's solid surface.

Space stations are constantly in a free-fall situation, which means their acceleration is the same as the local gravitational acceleration. As a result, neither the astronauts nor the other space station residents can feel the support force generated by the station's solid surface.

Thus, by rotating the space station around its center, we produce center-directed forces from the space station's wall in the absence of gravity.

Gravitational acceleration is equal to centripetal acceleration.

A = g

r2 = g r 2 = /g r 2 = 9.81 m s 2/ 55 m 2 = 0.178 r a d 2 s/ 2 = 0.422 r a d / s

Therefore, the angular speed of the space station is 0.422 rad/s.

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Hooke's law states that the applied force F equals a constant k times the displacement or change in length x.

What is Hooke's law?

The force necessary to extend or compress a spring by a certain distance scales linearly with respect to that distance, according to Hooke's law, an empirical law in physics.

Hooke's Law is a principle of physics that states that the that the force needed to extend or compress a spring by some distance.

F = K.x

A straight line passing through the origin can be drawn by plotting the spring's stretch versus the weight that has been applied to the hanger. This implies that a spring's extension is inversely proportional to the force used to stretch it.

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Answer:

si unit of force is Newton or dyne

The net charge on the sphere is 3.7×10⁻⁵C and the total electric flux leaving the surface of the sphere is 4.1×10⁶ N.m²/C.

The distribution of the electric field or the velocity at which the electric field moves through a specific area can both be measured as electric flux. The Greek letter is used to represent electrical flux. Voltmeters (Vm), often known as Nm 2 C – 1, is the SI unit for electric flux.

Procedure:

(a) The charge on the surface of the sphere is the product of the surface charge density σ and the surface area of the sphere which is 4πr².

Thus, q=4πr²σ

= 4π(1.2m/2)²(8.1×10⁻⁶)

=3.7×10⁻⁵C

(b) We select a spherical-shaped Gaussian surface with a slightly greater radius that is concentric with the conducting sphere.

∅=q/∈°

= 4.1×10⁶ N.m²/C

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If we were to make copies of musical content up to the 6th time, Mp3 players would have better sound quality because they have digital signals to produce sound, which do not deteriorate over time.

Cassette tapes work on analog magnetic tape recording format for recording audio and playback whereas mp3 is a type of digital technology that has digital signals to produce sound. This is the reason why cassettes do not sound better than digital mp3 players.

Cassette tapes being magnetic type media suffer from print which causes to hear a bit of sound before the sound is even started and result in deterioration over time whereas digital signals do no deteriorate over time.

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Gauge pressure required in city water mains for a stream is 147,150 Pa

In fluid mechanics, Bernoulli's principle states that an increase in fluid velocity occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. This principle is named after the Swiss mathematician Daniel his Bernoulli published it in his 1738 book Fluid Mechanics.

According to the Bernoulli's Equation:

P₁ + ρgy₁ + ([tex]\frac{1}{2}[/tex])ρv₁² = P₂ + ρgy₂ + ([tex]\frac{1}{2}[/tex])ρv₂²

where, y₁ =  initial height

y₂ = final height

Initial height is 0 meters and final height is 15 meters.

The problem states that the mains have a much larger diameter than the hose, so v₁ = 0

Once our water reaches a 15 m. altitude, it stops going anymore higher. Therefore, v₂ also be 0.

P₁  = P₂ + ρgy₂

Since, we are solving for gauge pressure, we can assume that the pressure at the top of our column of water is zero.

P₁  = ρgy₂

P₁  = 1000 × 9.8 × 15

P₁  = 147,150 Pa

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The weight of the car is 14308 Newtons and the net force acting on it is 230 N. The free body diagram is attached with the answer.

A drag is force that opposes the motion of an object by acting in the direction opposite to its motion.

Given is a car on the freeway that is traveling north at 55 mph on a straight and flat part of the road. The mass of the car is 1460 kg. The engine is pushing the car forward with a force of 760 N. while the drag on the car is 530 N.

PART - A

The free body diagram is attached with the answer. The following equations will help in mathematical analysis.

F[engine] - F[drag] = ma

a = {F[engine] - F[drag]}/m

and

W = N = mg

PART - B

The weight of the car can be calculated as follows -

W = mg = 1460 x 9.8 = 14308 Newton

PART - C

Net force on the car [F] = Force provided by engine {F[E]} - drag force {F[D]}

F = 760 - 530 = 230 N

The direction of force is towards north.

Therefore, the weight of the car is 14308 Newtons and the net force acting on it is 230 N. The free body diagram is attached with the answer.

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Here, if take it that you mean "perfectly smooth" to mean that there is no friction. If that is the case, then the box begins to move whenever there is a net horizontal force acting on it. (D) It goes without saying that the force increases as the box accelerates.

F = ma

Where, F is the force on the box and m is the mass of the box and a is the acceleration.

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-1.6 N

Split the forces into those in the x-direction and those in the y-direction. Since the book is not accelerating upward or downward, the net force in the y-direction is zero. Add the two forces in the x-direction (applied force and kinetic friction). This is the net force.

See details:

Electromagnetic radiation with the highest energy and shortest wavelength is a gamma ray. When radioactive atomic nuclei disintegrate, gamma rays are generated.

Gamma radiation causes atoms to lose their electrons. As a result, they are classified as ionizing radiation. Studies have shown that radiation can damage DNA, and that this damage can lead to cancer.

In certain cases, extreme exposure can cause cancer or even death. Some tiny microorganisms (bacteria, archaea, and fungi, together referred to as "microbes") have evolved radiation tolerance, despite the fact that gamma radiation can be extremely deadly for humans.

It is common practise to utilise gamma radiation to destroy live things like cells and organisms.

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Sound and thermal energy are kind of energy which involve movement.

Energy is defined as the capacity of a physical system to perform work.

When a force, such as sound or pressure, causes an item or substance to vibrate, the result is sound energy. Waves of that energy pass through the substance. We refer to the sound waves as kinetic mechanical energy.

The energy present in a system that determines its temperature is referred to as thermal energy. Thermal energy flows as heat.

Sound energy and thermal energy are involve movement of the particle.

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The deceleration experienced by the 1075 N sky diver as he opened his parachute is 13.39 m/s²

Force = mass × acceleration

We know that deceleration is the acceleration of stopping objects. Thus,

Force (F) = mass (m) × deceleration (a)

Thus, we can obtain the deceleration of the sky diver as follow:

Force = mass (m) × deceleration (a)

1469 = 109.69 × a

Divide both sides by 109.69

a = 1469 / 109.69

a = 13.39 m/s²

Thus, the deceleration is 13.39 m/s²

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Answer:The two objects have different amounts of acceleration due to the mass of the two objects being different

Explanation: The mass will affect acceleration. The higher the mass, the slower the acceleration. The formula for acceleration is a = f/m or acceleration = force divided by mass. The acceleration is faster for the milk glass and slower for the plate with cookies because the plate with cookies has a higher mass than the glass of milk.

Answer:

Explanation:

Given:

m₁ = m  -  Mass of milk mug

m₂ = 222·m₁ = 222·m  -  Mass of a plate of biscuits

F₁ = F₂ = F

________________

a₂ / a₁ - ?

2 Newton's law:

a = F / m

a₁ = F / m₁ =  F / m

a₂ = F / m₂ =  F / (222·m)

a₁ / a₂ = (F·222·m) / (F·m) = 222

The acceleration of a mug of milk is 222 times the acceleration of a bowl of cookies

A charge of 4.8 x 10 5 C is present on each capacitor plate.

B. The capacitor has a 4.5 x 10 6 J energy capacity.

Describe the capacitor.

A capacitor is a device used to store electrical power and charge. It is composed of at least two separated electrical conductors. Although usually referred to as "electrodes," these electrical conductors are actually "capacitor plates." A capacitor is referred to as a "vacuum capacitor" if the space between capacitors is nothing more than a vacuum. However, the space is often filled with a dielectric, an insulating material. How much storage space a capacitor has is determined by its capacitance attribute.

A. Establishing the charge

Capacitor (C) = 4 F = 4 10 6

Voltage = 12 volts.

Charge (Q)  = ?

Q = CV

Q = 4×10¯⁶ × 12

Q = 4.8×10¯⁵ C

B. Measuring the amount of energy the capacitor has stored.

Voltage (V) equals 1.5 V.

Energy (E) =? E = 12CV Capacitor (C) = 4 F = 410 6

²\sE = ½ × 4×10¯⁶ × 1.5²

E = 2×10¯⁶ × 2.25\sE = 4.5×10¯⁶ J

A. There is 4.8 x 10 5 C B of charge on each capacitor plate. The capacitor has 4.5 x 10 6 J of stored energy.

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Change in momentum =  -1.9 kg m/s

Momentum is the vector quantity because it has both magnitude and direction.

Momentum is given as the product of mass and velocity. It is represented as P = mv. Here, P is the momentum, m is the mass and v is the velocity.

Given,

Momentum = MV

The difference between the initial and final momentum will be the change of magnitude of the momentum.

To find the change in momentum,

Taking M as common

= M (V - U)

= 0.10 (-12 - 7)

= 0.10(-19)

= -1.9 kg m/s

Hence, the change in magnitude of momentum is -1.9 kg m/s.

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The total distance travelled by the glider before it leaves the ground is 867 meters.

Velocity is the change in displacement divided by time taken. Here the displacement is unknown. The glider reaches its launch speed of 51.0 m/s after accelerating for 17.0 s. The velocity of the glider is 51.0 m/s and time taken is 17.0 s. The equation to calculate the total distance travelled by the glider before it leaves the ground is given below.

velocity = displacement/time

displacement = velocity*time

displacement = 17.0*51.0 = 867 meters

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The magnitude of the elevator's acceleration is 18.25 m/s².

The acceleration of the elevator is calculated as follows;

R = Fa - Fg

R = ma - mg

R = m(a - g)

where;

m = W/g

m = (545 N) / (9.8 m/s²)

m = 55.61 kg

ma = R + mg

ma = R + W

a = (R + W) /m

a = (470 + 545) / 55.61

a = 18.25 m/s²

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The low-density, cold disks seen around some stars are distinct from the dense, hot disks found around some other stars because of their varied densities, temperatures, and positions.

- About circumstellar disc :

- A circumstellar disc (or circumstellar disk) is an accretion disk of matter in orbit around a star that has the shapes of a torus, pancake, or ring. It is made up of gas, dust, planetesimals, asteroids, or impact fragments. They are the sources of material where planets may form around the young stars.

- Gaseous clouds gradually collapse under the pull of gravity to become stars. As they fall toward the protostar, the atoms and molecules in the gas impart a slight rotation. The protoplanetary disk, a rotating plate of gas and dust, is produced by this rotation, which also gives the star its spin.

- A rotating circumstellar disk of dense gas and dust known as a protoplanetary disk surrounds a young, newly formed star, a T Tauri star, or a Herbig Ae/Be star.

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Between these two charges, there is an electric field with a magnitude and direction of 10.8 x 105 N/C along AB.

In this issue, we must charge the fee. Twenty micro colums make up Q 1, and eight micro coulons make up Q 2. There is a 20 centimeter gap between these two charges. At point p, which is the intersection of the two charges, we must determine the net electric field. The electric field at point p points away from the charge because of the positive charge. He, let's assume that the electric field is even and that it is caused by the second charge, electric field point along the charge: q 2- and that is the electric field e 2.

The net electric field at point p is now equal to e 1 plus 2 and is represented by the symbol a. Consider the direction away from Question 1 as positive; hence, the direction to the right is a positive direction. The electric field owing to eq, 1 equals the column, constant k times, k 1 over 0.5 times r square, and similarly for eq, 2, where q, 1 and q 2 are the absolute magnitude of the charge, the net electric field at point p equals p over 0.5 r square 0.5 r square times.

The net electric field at point at the midpoint between the 2 charges, equals 2.52 times 10 to the 7 newtons co coulan and the direction will be towards the negative charge towards the minus 8 coulomb judge micro cholum charge. The sum of the absolute magnitude of the 2 charges and the electric field at point p equals 9 times 10 to the 9 newton meter square per column square over 0.5 times 0.2 meter square times, 20 plus 8 times 10 to the minus 6 couul Thus, at the halfway point between the t charges, this will be the net electric field.

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Yes, Speed is the magnitude of its velocity.

What is speed?
velocity is a vector, and Speed is a scalar (just a number). Whereas a velocity has both a direction and a magnitude. As I said, the magnitude of the velocity is known as the speed.

A moving object's speed is the distance it travels in a given length of time.  The average speed of an object in a given time is equal to the distance traveled divided by the time. The distance traveled by an object per unit of time is also known as its speed. When an object's speed changes, it becomes faster or slower. Acceleration occurs when the speed of an object increases. Deceleration, or negative acceleration, occurs when an object becomes slower as its speed drops.

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Buoyant force is greater than the Net Weight. Thus it will get off the ground.

Density is the substance which is defined as the measurement of the given mass per unit volume. It is represented by the formula

D = m/v

Where,

D = Density

m = Mass

v = Volume

Now

Helium Mass = Density × Volume

                      [tex]= 0.160\ kg/m^3 \times \frac{4}{3} \times \pi \times r^3\ m^3[/tex]

                     = 15.99 kg

Total Mass of the Balloon = Mass of the given Instruments + Mass of the given Helium Filled + Empty Mass of the given Balloon

Total Mass of the Balloon will be = 10.0 kg + 15.99 kg + 5.00 kg

                                                      = 30.99 Kg

Displaced air mass = Density × Volume

Displaced air mass [tex]= 1.16\ kg/m^3 \times \frac{4}{3} \times \pi \times r^3\ m^3[/tex]

                                = 115.89 Kg

Now,

Buoyant Force = Mass × 9.8

                        = 115.89 Kg × 9.8

Net Force = Mass × 9.8

                 = 30.99 kg × 9.8

Thus from the above conclusion we can say that the Buoyant force is greater than the Net Weight. Thus it will get off the ground.

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The efficiency of the heating system is 80%.

Efficiency is the regularly measurable capacity to keep away from losing substances, energy, effort, cash, and time in doing something or in producing the desired end result. In a greater popular experience, it is the capability to do things nicely, efficaciously, and without waste.

Heat pumps are the most efficient way to heat pretty much any enclosed area, they are quiet and comfy, they decrease your heating invoice considerably, and they double as an air-conditioning gadget in the summer. Fuel heating systems can be fueled with the aid of both herbal fuel and propane with easy adjustments accounting for the one-of-a-kind traits of every. We seek advice from each fuel as genuinely "gasoline." The maximum commonplace styles of structures encompass compelled air, warm water, steam, and localized space heating.

efficiency = output/input × 100

                = 320 / 400 × 100

                 = 80 %

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